Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, such as ax^n + bx^(n-1) + ... + k.

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means expressing it as a product of irreducible polynomials, meaning it cannot be factored further.

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or terms without leaving a remainder.

Front

How do you find the GCF of polynomial terms?

Back

To find the GCF of polynomial terms, identify the highest power of each variable common to all terms and multiply it by the GCF of the coefficients.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern expressed as a^2 - b^2 = (a - b)(a + b).

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

How do you factor a trinomial of the form x^2 + bx + c?

Back

To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n).

Front

What is the factoring method for the polynomial 10x^2 + 15x - 5?

Back

The polynomial can be factored as 5(2x^2 + 3x - 1).